There is no law requiring that you do so, but it is usually a good idea. Mold exists not only in the places where it is visible, but throughout the infected fruit, and can make you sick.
Yes, you should throw away moldy fruit. Although some areas of the fruit may appear to be free of mold, there are most likely mold spores that cannot be seen.
It depends on how large the mold part is. Generally if it is only very small mold, you do not need to give away the whole fruit,otherwise you should do that for fear of not getting ill.